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Plasmas The “Fourth State” of the Matter • The matter in “ordinary” conditions presents itself in three fundamental states of aggregation: solid, liquid and gas. • These different states are characterized by different levels of bonding among the molecules. • In general, by increasing the temperature (=average molecular kinetic energy) a phase transition occurs, from solid, to liquid, to gas. • A further increase of temperature increases the collisional rate and then the degree of ionization of the gas. The “Fourth State” of the Matter (II) • The ionized gas could then become a plasma if the proper conditions for density, temperature and characteristic length are met (quasineutrality, collective behavior). • The plasma state does not exhibit a different state of aggregation but it is characterized by a different behavior when subjected to electromagnetic fields. The “Fourth State” of the Matter (III) Debye Shielding • An ionized gas has a certain amount of free charges that can move in presence of electric forces Debye Shielding (II) • Shielding effect: the free charges move towards a perturbing charge to produce, at a large enough distance lD, (almost) a neutralization of the electric field. lD E E~0 Debye Shielding (IV) • The quantity lDe 0 k BT nqe2 is called the (electron) Debye length of the plasma • The Debye length is a measure of the effective shielding length beyond which the electron motions are shielding charge density fluctuations in the plasma Debye Shielding (IV) • Typical values of the Debye Length under different conditions: n [m-3] Interstellar Solar Wind Solar Corona Solar atmosphere Magnetosphere Ionosphere 106 107 1012 1020 107 1012 T[eV] 10-1 10 102 1 103 10-1 Debye Length [m] 1 10 10-1 10-6 102 10-3 From Ionized Gas to Plasma • An ionized gas is characterized, in general, by a mixture of neutrals, (positive) ions and electrons. • For a gas in thermal equilibrium the Saha equation gives the expected amount of ionization: 3/2 Ui / kBT n 2.4 10 nnT e 2 i 21 • The Saha equation describes an equilibrium situation between ionization and (ion-electron) recombination rates. From Ionized Gas to Plasma (II) • (Long range) Coulomb force between two charged particles q1 and q2 at distance r: q1q2 F 4 0 r 2 q1 q2 r From Ionized Gas to Plasma (III) • (Short range) force between two neutral atoms (e.g. from Lenard-Jones interatomic potential model) r repulsive attractive From Ionized Gas to Plasma • If L is the typical dimension of the ionized gas, a condition for an ionized gas to be “quasineutral” is: lD L • The “collective effects” are dominant in an ionized gas if the number of particles in a volume of characteristic length equal to the Debye length (Debye sphere) is large: 4 3 N D n lD 1 3 • ND is called “plasma parameter” From Ionized Gas to Plasma (II) • A plasma is an ionized gas that is “quasineutral” and is dominated by “collective effects” is called a plasma: lD L 4 3 N D n lD 1 3 From Ionized Gas to Plasma (III) • An ionized gas is not necessarily a plasma • An ionized gas can exhibit a “collective behavior” when the long-range electric forces are sufficient to maintain overall neutrality • An ionized gas could appear quasineutral if the charge density fluctuations are contained in a limited region of space • A plasma is an ionized gas that exhibits a collective behavior and is quasineutral Plasma Confinement: the Lorentz Force Force on a charged particle in a magnetic field F=qvxB Plasma Confinement: the Magnetic Mirror Magnetic Mirror: charged particles (protons and electrons) move in helical orbits at their cyclotron frequency